The game controller spec for MFi partners is a framework, according to those familiar with Apple's plans. It's a template for one of two specific sets of controller types: a "standard" controller with a d-pad, four buttons, and left/right shoulder buttons, and an "extended" game controller with two analog pads and two sets of shoulder buttons. You can see examples of each above. Either spec could be designed as a snap-on case accessory connected via Lightning, a stand-alone wireless AirPlay controller, or whatever other design an accessory-maker saw fit.
I'm surprised that this hasn't been more widely reported, but it's certainly a big deal, and appears well-thought-through from what we know so far. I've said before that I think an upgraded iPod nano could work great as a Bluetooth remote for the Apple TV, but this offers the hope of real gaming controllers for a future—App enabled—iOS device hanging off our HD TV screens.